Related papers: Smoothed analysis of complex conic condition numbe…
We develop constrained Bayesian estimation methods for small area problems: those requiring smoothness with respect to similarity across areas, such as geographic proximity or clustering by covariates; and benchmarking constraints,…
This paper is devoted to a structured perturbation analysis of the symmetric algebraic Riccati equations by exploiting the symmetry structure. Based on the analysis, the upper bounds for the structured normwise, mixed and componentwise…
Spielman and Teng introduced the smoothed analysis of algorithms to provide a framework in which one could explain the success in practice of algorithms and heuristics that could not be understood through the traditional worst-case and…
We introduce an arbitrary order, computationally efficient method to smooth corners on curves in the plane, as well as edges and vertices on surfaces in $\mathbb R^3$. The method is local, only modifying the original surface in a…
The purpose of this paper is to establish bounds on the rate of convergence of the conjugate gradient algorithm when the underlying matrix is a random positive definite perturbation of a deterministic positive definite matrix. We estimate…
We investigate border ranks of twisted powers of polynomials and smoothability of symmetric powers of algebras. We prove that the latter are smoothable. For the former, we obtain upper bounds for the border rank in general and prove that…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
We study a class of conditional independence models for discrete data with the property that one or more log-linear interactions are defined within two different marginal distributions and then constrained to 0; all the conditional…
Machine learning has recently emerged as a fruitful area for finding potential quantum computational advantage. Many of the quantum enhanced machine learning algorithms critically hinge upon the ability to efficiently produce states…
Let $M$ be an arbitrary $n$ by $n$ matrix of rank $n-k$. We study the condition number of $M$ plus a \emph{low-rank} perturbation $UV^T$ where $U, V$ are $n$ by $k$ random Gaussian matrices. Under some necessary assumptions, it is shown…
In this paper we address smoothing-that is, optimisation-based-estimation techniques for localisation problems in the case where motion sensors are very accurate. Our mathematical analysis focuses on the difficult limit case where motion…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
The smallest singular value and condition number play important roles in numerical linear algebra and the analysis of algorithms. In numerical analysis with randomness, many previous works make Gaussian assumptions, which are not general…
In this paper, we present a new smoothing approach to solve general nonlinear complementarity problems. Under the $P_0$ condition on the original problems, we prove some existence and convergence results . We also present an error estimate…
Smoothed analysis is a method for analyzing the performance of algorithms, used especially for those algorithms whose running time in practice is significantly better than what can be proven through worst-case analysis. Spielman and Teng…
Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…
Conditional stability estimates require additional regularization for obtaining stable approximate solutions if the validity area of such estimates is not completely known. In this context, we consider ill-posed nonlinear inverse problems…
This paper presents a method for mathematical modelling of surfaces conditioned on empirical data. It is based on solving a discrete biharmonic equation over a domain with given inner point and inner curve data. The inner curve data is used…
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We…
We show that the smoothed complexity of the logarithm of Renegar's condition number is O(log (n/sigma)).